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Font ligatures and Unicode symbols

1. Why this matters

Lex documents lean heavily on arrows and logical symbols. ->, <-, =>, !=, <=>, ... appear constantly — not just in technical specs but in everyday prose: cause and effect, logical implication, ranges, approximate values, ellipses.

Authors writing Lex in a ligature-aware monospace font (Geist Mono, Fira Code, JetBrains Mono) see these ASCII sequences rendered as proper typographic symbols. The source stays ASCII on disk, but the screen shows → ⇒ ≠ ⇔ …

The problem is that rendering is purely local to the author's editor. When the document ships — to a coworker opening the HTML in Chrome, a student viewing the PDF, a reviewer on a different OS — the ligatures vanish. -> becomes a dash followed by a greater-than sign. The visual clarity the author relied on is gone.

Lex is meant to reach beyond technical authoring environments. The reader viewing a Lex-generated HTML file should see the same typographic symbols the author saw, regardless of whether they have a programmer's font installed. This document surveys which ASCII-to-symbol mappings can be done at the text layer (via Unicode substitution) versus which require a controlled font layer (via embedded webfonts with OpenType ligature features).

2. The tiers

Symbols split into three tiers based on how reliably they render across fonts. Tier 2 splits further by Unicode block, because the practical coverage story is different for each half.

2.1. Tier 1 — universal

Codepoints in the oldest BMP blocks: Arrows (U+2190–U+21FF core range), basic Mathematical Operators (U+2200–U+22FF), General Punctuation (U+2000–U+206F). Present in every mainstream font — OS defaults, Google Fonts text families, bare system fallbacks like DejaVu and Liberation. Safe to substitute unconditionally in prose.

2.2. Tier 2a — widespread

Codepoints in the upper Arrows block (U+219C–U+21DD) and extended Mathematical Operators (U+2254, U+2262), plus the interrobang (U+203D). Added in early Unicode versions and carried by all text-optimized fonts: Arial, Helvetica, Roboto, Inter, Open Sans, Lato, Source Sans, Noto Sans. Safe to substitute when targeting mainstream fonts; occasional fallback in older or display-focused typefaces.

2.3. Tier 2b — spotty

Codepoints in Supplemental Arrows-A (U+27F5–U+27FA) — the long-form arrows. Coverage is inconsistent. Arial and Helvetica historically do not cover these; the browser falls back to a math-capable font (STIX, Cambria Math), rendering the glyph at a mismatched weight and baseline. Inter, Noto Sans, SF Pro, and Segoe UI cover them cleanly. Substitute only when the font is controlled via @font-face.

2.4. Tier 3 — font-only

No reliable Unicode equivalent. These ligatures exist only as font-level OpenType substitutions (calt / liga features). The ASCII sequence must stay as-is in the source; visual rendering is entirely the font's responsibility.

3. Tier 1 substitutions

Safe for every output, every font, every reader

ASCII Symbol Codepoint Name
-> → U+2192 Rightwards arrow
<- ← U+2190 Leftwards arrow
<-> ↔ U+2194 Left right arrow
=> ⇒ U+21D2 Rightwards double arrow
<=> ⇔ U+21D4 Left right double arrow
<= ≤ U+2264 Less than or equal
>= ≥ U+2265 Greater than or equal
!= ≠ U+2260 Not equal
/= ≠ U+2260 Not equal
=/= ≠ U+2260 Not equal
=== ≡ U+2261 Identical to
~~ ≈ U+2248 Almost equal to
~= ≃ U+2243 Asymptotically equal
... … U+2026 Horizontal ellipsis
-- – U+2013 En dash
--- — U+2014 Em dash

4. Tier 2a substitutions

Safe in any text-optimized font (Arial, Helvetica, Roboto, Inter, Open Sans, Lato, Source Sans, Noto Sans)

ASCII Symbol Codepoint Name
:= ≔ U+2254 Colon equals
!== ≢ U+2262 Not identical to
!? ‽ U+203D Interrobang
->> ↠ U+21A0 Two-headed rightwards
>-> ↣ U+21A3 Rightwards arrow with tail
~> ⇝ U+21DD Rightwards squiggle arrow
<~ ↜ U+219C Leftwards wave arrow
<~> ↭ U+21AD Left right wave arrow
<<- ↞ U+219E Two-headed leftwards

One additional Tier 2a mapping is worth noting but sits outside the table because | is the Lex cell delimiter: the bar-hyphen-greater sequence (written in ASCII as pipe followed by ->) maps to ↦ (U+21A6, Maps to) — the functional "mapsto" arrow common in type signatures and mathematical writing.

5. Tier 2b substitutions

Use only when an embedded webfont with Supplemental Arrows-A coverage is guaranteed. Without that guarantee, these render in a fallback font and look visually worse than plain ASCII

ASCII Symbol Codepoint Name
--> ⟶ U+27F6 Long rightwards arrow
<-- ⟵ U+27F5 Long leftwards arrow
==> ⟹ U+27F9 Long rightwards double arrow
<== ⟸ U+27F8 Long leftwards double arrow
<==> ⟺ U+27FA Long left right double arrow

6. Tier 3 — font-only

No reliable Unicode equivalent. Leave as ASCII and rely on an embedded ligature font (or on the reader having one installed) if you want the glyph rendering.

Representative examples
  • ==, =>>, =<<
  • >=>, >>=, >>-, >-
  • -<, -<<, <=<, <<=, <-<
  • <|, <||, <|||, <|>, |||>, ||=, ||>, |>, |=
  • |}, {|, </>, <!--, <>
  • ~@, ~-, -~, ~~>, <~~
  • ###, %%, .=, ..=, ??, ???

7. Font coverage comparison

Coverage of each tier across common font families. ✓ = reliable coverage, ~ = partial (browser fallback likely for some codepoints), ✗ = no coverage, liga = rendered via OpenType liga / calt rather than via dedicated Unicode codepoints

Font family Tier 1 Tier 2a Tier 2b Tier 3
Arial ✓ ✓ ✗ ✗
Helvetica / Helvetica Neue ✓ ✓ ✗ ✗
Times New Roman ✓ ✓ ✗ ✗
Courier New ✓ ~ ✗ ✗
SF Pro (macOS system) ✓ ✓ ✓ ✗
Segoe UI (Windows system) ✓ ✓ ✓ ✗
Roboto ✓ ✓ ~ ✗
Inter ✓ ✓ ✓ ✗
Open Sans ✓ ✓ ~ ✗
Lato ✓ ✓ ~ ✗
Source Sans 3 ✓ ✓ ~ ✗
Noto Sans ✓ ✓ ✓ ✗
Merriweather / Playfair (serif display) ✓ ~ ✗ ✗
Fira Code ✓ ✓ ✓ liga
JetBrains Mono ✓ ✓ ✓ liga
Geist Mono ✓ ✓ ✓ liga
Cascadia Code ✓ ✓ ✓ liga
A few notes on reading the table
  • The ~ cells are the trap. The glyph renders, but not in the requested font — the browser silently swaps to a math fallback with a different weight and baseline. Visually it's worse than leaving the ASCII alone.
  • The display serifs row illustrates why typeface choice matters beyond aesthetics: a heading font that looks beautiful for titles may fail on body text that contains Tier 2 symbols.
  • Monospace ligature fonts are the only place Tier 3 sequences render as symbols, and they do it via OpenType features, not Unicode substitution.

8. Recommendation

Two layers, applied together:

Text layer (Unicode substitution pass in the HTML/PDF formatter, applied to prose only — never inside verbatim blocks or inline code)
  • Always apply Tier 1.
  • Apply Tier 2a when the document's font stack leads with a widespread text font or embedded webfont.
  • Apply Tier 2b only when an embedded webfont with Supplemental Arrows-A coverage is guaranteed via @font-face.
  • Never substitute Tier 3. Leave ASCII; let the font do the work or let it stay literal.
Font layer (for readers who want full ligature fidelity regardless of their system)
  • Embed a ligature-capable font via @font-face in HTML output. Geist Mono and JetBrains Mono are both OFL-licensed and cover Tier 3 cleanly.
  • Enable font-feature-settings: "liga", "calt"; on code and verbatim blocks.
  • This closes the Tier 3 gap and covers any Tier 2 misses without source transformation.
Config surface proposal
  • unicode_substitutions = "basic" | "extended" | "full" | "off"
  • basic applies Tier 1 only (default).
  • extended adds Tier 2a.
  • full adds Tier 2b (requires embedded font guarantee).
  • off disables substitution entirely; ASCII ships as written.

The guiding principle: substitution should never produce a worse rendering than the ASCII it replaces. Tier 1 never does. Tier 2a rarely does. Tier 2b will, unless the font is pinned. Tier 3 always does.